On the Application of Modified Finite Sine Transform to Structural Mechanics

Abstract

The method of modified finite sine transform (MFST) was introduced to solve fourth-order boundary value problems in structural mechanics. The analytical features and computational aspects of MFST were presented, including integral transforms of the derivatives of functions and the term-by-term differentiation of inverse MFST. For the simplicity of demonstrating the solution process, the cantilever beam was used in the discussion. Numerical results for transverse vibration based on the present method were compared and validated with existing results for natural frequencies. Although the present method is not superior to conventional finite sine transform method in one-dimensional structures, it could be significantly efficient for two-dimensional structures with asymmetric boundary conditions, especially including cantilever plates and other plates with only one free edge or two adjacent free edges.